Sunday, April 15, 2018 - Saturday, April 21, 2018

Topology

Title: A New Algorithm in Group Theory

Date: 04/16/2018

Time: 4:10 PM - 5:30 PM

Place: C304 Wells Hall

Speaker: Rita Gitik

We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a weakly Nielsen generating set of a subgroup. We also give a new proof of decidability of a membership problem for quasiconvex subgroups of negatively curved groups.

Applied Mathematics

Quantifying the intrinsic structure from a given massive dataset, which is often nonlinear and complex, is a common challenge shared in almost all scientific fields, including data science. The problem is becoming more challenging when the data are from multiple sensors with heterogenous data types. The diffusion geometry is a flexible framework for this challenge that has led to several convincing results with solid theoretical backup. We will discuss how to apply the diffusion geometry, particularly the alternating diffusion and commutator, to deal with the sensor fusion problem. Its application to the sleep dynamics analysis and fetal electrocardiogram analysis will be discussed.